Jucys--Murphy elements and representations of cyclotomic Hecke algebras

O. V. Ogievetsky, L. Poulain d'Andecy

Published 2012-06-04, updated 2012-06-18Version 2

An inductive approach to the representation theory of cyclotomic Hecke algebras, inspired by Okounkov and Vershik, is developed. We study the common spectrum of the Jucys-Murphy elements using representations of the simplest affine Hecke algebra. Representations are constructed with the help of a new associative algebra whose underlying vector space is the tensor product of the cyclotomic Hecke algebra with the free associative algebra generated by standard m-tableaux.